Theorem 1.1 
Suppose \(n\ge 4\) . Let \(U\subset  be a connected open subset, and \) f:U be a \(W^{1,p}_{\operatorname{loc}}\) -mapping for \(p>\nu \) , such that the Pansu differential is an isomorphism almost everywhere. Then \(f\)  is the restriction of a diffeomorphism \( of the form \) g\( where \) gGL(n,R)\(, \) {0,1}\(.\) 
In the theorem and below we use the convention that \(\psi ^0=\operatorname{id}\)  and \(\psi ^1=\psi \) .
Note that the rigidity assertion is false when \(n=3\) , because \((W)\)  is locally equivalent to the Heisenberg group, and hence has an infinite dimensional group of contact diffeomorphisms, which are all Sobolev mappings with nondegenerate Pansu differential. Quasiconformal homeomorphisms
are \(W^{1,p}_{\operatorname{loc}}\) -mappings for some \(p>\nu \)  [1]}, and therefore we obtain:
